Cooling system first, unless you want to risk doing the head gasket job twice.
Stock radiators are okay as long as you keep ahead of them, putting in a new one before the plastic end tanks and connections get brittle. The stock fan is usually enough with the stock radiator to keep these cars cool on track, but not always. The stock fans seem to be a bit random. I spend Friday night until midnight two weeks ago holding a light so Tommy could change the fan and radiator on his E36 M3 track car, after his new-ish stock fan grenaded into the radiator Friday afternoon on track. I would dump the stock fan and switch to electric with a Mishimoto radiator, just to stamp paid to the whole concern.
Engine bay fuel lines -- they are long and high pressure and rubber and old. I am afraid of car fires, based on a friend's awful luck. I am also suspicious of fuel filters on old cars and I tend to replace them unless I know the previous owner was anal.
Some people say the oil pump retaining nut should be pinned or welded. I wouldn't remove the oil pan just for that job because it's pretty hard, unless the motor is out. If the motor is out, I would do it and replace the oil pan gasket.
If you are running stock dampers and springs, you can probably put off all the rear bushings until you get something with less wobble and roll. Don't forget rear trailing arm pocket reinforcement plates, which need to be welded on. Don't forget rear subframe bushings. For the rear subframe bushings and the rear trailing arm bushings, I personally believe OEM is not stiff enough for precise handling at 1.0G, and these cars are easily capable of 1.2G. Ish. For rear control arm bushings, I now use these, and only these exactly, they are the most durable I have found with the best design: AC Delco RCAB. If you use urethane RTABs, you don't need (or want) the RTAB limiter discs.
Some people have managed to break the mounting bolt on the front/nose end of the differential. This may be related to use of OEM differential mounts at all three positions. In my case, I put it pretty far down the list of things to worry about.
Guibo and center support bearing -- inspect but no need to replace unless they look or sound sketchy. But I carried spares because the first sign of flaky-ness will manifest on the first day of a track weekend.
Front control arms, lolipop/bushings, and tie rod ends. My car had pretty stable steering, so I STILL haven't done these, even though I have the parts on hand. I suggest you swap the front damper mounts (right side to left side and vice versa). It will give a nice amount of negative camber, which these cars need.
The Track/Autocross forum on Bimmerforums is a wealth of experience with pretty much any part or combination you can imagine. Usually I get info from actual experience not just with the specific parts, but how they performed on my specific tracks.
